Basic Math Examples

0 - {(\sqrt{100 - (a + 4)})}^{2}

$0 - {(\sqrt{100 - (a + 4)})}^{2}$

Step 1

Subtract

{(\sqrt{100 - (a + 4)})}^{2}

${(\sqrt{100 - (a + 4)})}^{2}$ from

0

$0$ .

- {(\sqrt{100 - (a + 4)})}^{2}

$- {(\sqrt{100 - (a + 4)})}^{2}$

Step 2

Apply the distributive property.

- {\sqrt{100 - a - 1 \cdot 4}}^{2}

$- {\sqrt{100 - a - 1 \cdot 4}}^{2}$

Step 3

Simplify the expression.

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Step 3.1

Multiply

- 1

$- 1$ by

4

$4$ .

- {\sqrt{100 - a - 4}}^{2}

$- {\sqrt{100 - a - 4}}^{2}$

Step 3.2

Subtract

4

$4$ from

100

$100$ .

- {\sqrt{- a + 96}}^{2}

$- {\sqrt{- a + 96}}^{2}$

- {\sqrt{- a + 96}}^{2}

$- {\sqrt{- a + 96}}^{2}$

Step 4

Factor

- 1

$- 1$ out of

- a + 96

$- a + 96$ .

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Step 4.1

Factor

- 1

$- 1$ out of

- a

$- a$ .

- {\sqrt{- (a) + 96}}^{2}

$- {\sqrt{- (a) + 96}}^{2}$

Step 4.2

Rewrite

96

$96$ as

- 1 (- 96)

$- 1 (- 96)$ .

- {\sqrt{- (a) - 1 (- 96)}}^{2}

$- {\sqrt{- (a) - 1 (- 96)}}^{2}$

Step 4.3

Factor

- 1

$- 1$ out of

- (a) - 1 (- 96)

$- (a) - 1 (- 96)$ .

- {\sqrt{- (a - 96)}}^{2}

$- {\sqrt{- (a - 96)}}^{2}$

- {\sqrt{- (a - 96)}}^{2}

$- {\sqrt{- (a - 96)}}^{2}$

Step 5

Rewrite

{\sqrt{- (a - 96)}}^{2}

${\sqrt{- (a - 96)}}^{2}$ as

- (a - 96)

$- (a - 96)$ .

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Step 5.1

Use

\sqrt[n]{a^{x}} = a^{\frac{x}{n}}

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

\sqrt{- (a - 96)}

$\sqrt{- (a - 96)}$ as

{(- (a - 96))}^{\frac{1}{2}}

${(- (a - 96))}^{\frac{1}{2}}$ .

- {({(- (a - 96))}^{\frac{1}{2}})}^{2}

$- {({(- (a - 96))}^{\frac{1}{2}})}^{2}$

Step 5.2

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

- {(- (a - 96))}^{\frac{1}{2} \cdot 2}

$- {(- (a - 96))}^{\frac{1}{2} \cdot 2}$

Step 5.3

Combine

\frac{1}{2}

$\frac{1}{2}$ and

2

$2$ .

- {(- (a - 96))}^{\frac{2}{2}}

$- {(- (a - 96))}^{\frac{2}{2}}$

Step 5.4

Cancel the common factor of

2

$2$ .

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Step 5.4.1

Cancel the common factor.

- {(- (a - 96))}^{\frac{2}{2}}

$- {(- (a - 96))}^{\frac{2}{2}}$

Step 5.4.2

Rewrite the expression.

- {(- (a - 96))}^{1}

$- {(- (a - 96))}^{1}$

- {(- (a - 96))}^{1}

$- {(- (a - 96))}^{1}$

Step 5.5

Simplify.

- - (a - 96)

$- - (a - 96)$

- - (a - 96)

$- - (a - 96)$

Step 6

Apply the distributive property.

- (- a - - 96)

$- (- a - - 96)$

Step 7

Multiply

- 1

$- 1$ by

- 96

$- 96$ .

- (- a + 96)

$- (- a + 96)$

Step 8

Apply the distributive property.

- - a - 1 \cdot 96

$- - a - 1 \cdot 96$

Step 9

Multiply

- - a

$- - a$ .

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Step 9.1

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

1 a - 1 \cdot 96

$1 a - 1 \cdot 96$

Step 9.2

Multiply

a

$a$ by

1

$1$ .

a - 1 \cdot 96

$a - 1 \cdot 96$

a - 1 \cdot 96

$a - 1 \cdot 96$

Step 10

Multiply

- 1

$- 1$ by

96

$96$ .

a - 96

$a - 96$

⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$